Automated Customization of Loudspeakers

ABSTRACT

A loudspeaker includes a horn including a first end panel, a second end panel, a first side panel, and a second side panel. Edges of at least the first and second side panels define a diffraction slot opening. The first and second side panels are each fabricated from a sheet of flexible material held in a stressed, curved shape by at least a rigid support member. The panels are designed by an automated process based on a number of electro-acoustic transducers to be used in a loudspeaker, horizontal and vertical coverage angles for the loudspeaker, and a wall length for a horn of the loudspeaker.

This application is a divisional of U.S. patent application Ser. No.12/557,885 filed on Sep. 11, 2009 and titled “Automated Customization ofLoudspeakers.”

BACKGROUND

This disclosure relates to automated customization of loudspeakers.

Audio reproduction systems for large venues typically use arrays ofmodular loudspeakers to produce the level and distribution of soundenergy necessary to fill the venue with sound. In some examples, one-offcustom loudspeakers that attempt to fill a portion of the venue with asingle loudspeaker may be fabricated based on a designer's estimate ofthe proper dimensions for such a loudspeaker.

SUMMARY

In general, in some aspects, a loudspeaker includes a horn including afirst end panel, a second end panel, a first side panel, and a secondside panel. Edges of at least the first and second side panels define adiffraction slot opening. The first and second side panels are eachfabricated from a sheet of flexible material held in a stressed, curvedshape by at least a rigid support member.

Implementations may include one or more of the following features. Thefirst and second end panels each include a rigid sheet material. Thediffraction slot opening has a convex curvature relative to the insideof the horn. The side panels are curved in a direction corresponding tothe diffraction slot opening while remaining straight in a directionperpendicular to the slot opening. The curved shapes of the first andsecond side panels each have dimensions corresponding to a section of aright circular conical surface. The conical surface section is boundedby a first circular arc of a first radius, a second circular arc of asecond radius, and straight edges collinear with lines on the conicalsurface that intersect an end of each of the first and second circulararcs and the apex of the cone. The conical surface section is bounded bya first circular arc of a first radius, a second arc of a varyingradius, and straight edges collinear with lines on the conical surfacethat intersect an end of each of the first and second arcs and the apexof the cone. The first and second side panels have dimensions when flatcorresponding to a section of a planar annulus defined by an innerradius, an outer radius, and an angle. The first and second side panelseach vary in length and curvature along the extent of the slot opening.The first and second side panels each include a first edge, and thefirst edges of the side panels are each coupled to the rigid supportmember under tension and without fasteners along the length of the firstedge. The first edges of the side panels are each coupled to the rigidspine member at an angle that varies along the length of the first edge.

The loudspeaker includes a plurality of manifold components, each havingan output opening coupled to the diffraction slot opening, the outputopenings of the plurality of manifold components together constituting adiffraction slot source at the diffraction slot opening; and a pluralityof electro-acoustic transducers, each coupled to an input opening of oneof the manifold components. The manifold components each have two inputopenings and include two acoustic passages, each of the acousticpassages having a first end at a different one of the two input openingsand a second end at the output opening, and the acoustic passages eachcurving away from the output opening in a different direction, such thatthe input openings are located near opposite sides of the horn. Themanifold components each have one input opening and include one acousticpassage having a first end at the input opening and a second end at theoutput opening, the acoustic passage of each manifold component curvingaway from the output opening in a direction opposite that of theneighboring manifold components' acoustic passages, such that the inputopening is located near the opposite side of the horn from theneighboring manifold components' input openings.

In general, in some aspects, a process obtains loudspeaker dataidentifying a number of electro-acoustic transducers to be used in aloudspeaker, horizontal and vertical coverage angles for theloudspeaker, and a wall length for a horn of the loudspeaker. Theprocess computes a curvature of a diffraction slot of the loudspeakerhaving a length based on the number of transducers, defines top andbottom end panels of the horn of the loudspeaker corresponding to thevertical coverage angle, defines first and second side walls of the hornhaving lengths, widths, and curvatures based on the number oftransducers, the horizontal and vertical coverage angles, and thecurvature of the diffraction slot, computes dimensions of flat panelscorresponding to the defined first and second side walls, and outputsmachine-readable plans for fabrication of the top and bottom end panelsand the first and second side walls.

Implementations may include one or more of the following features. Flatpanels are fabricated based on the output plans, and assembled to formthe horn. Fabricating the flat panels includes inputting the plans to aCNC milling machine, and operating the CNC milling machine to cut panelsof thin flexible material according to the plans. The thin flexiblematerial includes PVC. Assembling the flat panels to form the hornincludes securing first and second edges of each of the side wall panelsto first and second edges of the top and bottom end panels, and bendingthe side wall panels to conform a third edge of each of the side wallpanels to the computed curvature. Bending the side wall panels includessecuring a first one of the top or bottom end panel to a first end of acurved support structure corresponding to the computed curvature, anddrawing the other of the top or bottom end panel toward a second end ofthe curved support structure, such that the third edges of each of theside wall panels each seat in a groove in the curved support structure.

A keel including a curved support structure corresponding to thecomputed curvature is assembled. A plurality of manifold components arefixed to the support structure, each having an output opening positionedwithin the support structure, where the output openings of the pluralityof manifold components together form a diffraction slot source. Aplurality of electro-acoustic transducers are each fixed to one of themanifold components, each transducer coupled to an input opening of thecorresponding manifold component. The keel is coupled to a horn,fabricated according to the plans, such that the diffraction slot sourceis coupled a diffraction slot opening in the horn defined by edges of atleast the first and second side panels.

Defining the first and second side walls includes computing a radius R₁of an inner circumference of an annulus, a radius R₂ of an outercircumference of the annulus, and an angle V_(f) of a section of theannulus, the side walls each corresponding to a section of the annulusbounded by the computed angle. The radius R₁ is computed by applying theformula

${R_{1} = \frac{B}{2{\sin \left( {\frac{1}{2}\frac{V}{N}} \right)}{\cos \left( \frac{H}{2} \right)}}},$

where B is a dimension of one of the transducers, H is an angle betweenplanes connecting the location of the loudspeaker to sides of thecoverage area, V is an angle between planes connecting the location ofthe loudspeaker to the front and back of the coverage area, and N is thenumber of transducers. The radius R₂ is computed by applying the formulaR₂=R₁+L, where L is the length of the horn. The angle V_(f) is computedby applying the formula

${V_{f} = {V\mspace{14mu} {\cos \left( \frac{H}{2} \right)}}},$

where H is an angle between planes connecting the location of theloudspeaker to sides of the coverage area, and V is an angle betweenplanes connecting the location of the loudspeaker to the front and backof the coverage area.

Defining the first and second side walls includes modeling a set ofsub-horns each corresponding to a section of the diffraction slot andshaped to confine acoustic energy radiated by the section of thediffraction slot to a corresponding section of the coverage area, anddeforming and joining side walls of adjacent pairs of the trapezoidalsub-horns to define contiguous curved sheets spanning all of thesub-horns. Each of the sections of the coverage area corresponds to aprojected area perpendicular to a direction of radiation from thecorresponding section of the diffraction slot to the section, all of theprojected areas having substantially the same area. The curvature of thediffraction slot includes a circular arc. The curvature of thediffraction slot includes a curve having a progressively decreasingradius. Defining the side walls includes modifying the curvatures of theside walls based on data describing material properties of the sidewalls.

Obtaining the loudspeaker data includes receiving input data describinga venue, a location for the loudspeaker in the venue, a coverage areawithin the venue, and a sound pressure level associated with thecoverage area. The number of electro-acoustic transducers to be used inthe loudspeaker, the horizontal and vertical coverage angles, and thelength of the horn are all determined from the input data.

Determining the number of transducers includes receiving the number oftransducers as input from a user. Determining the number of transducersincludes computing an amount of acoustic power necessary to provide thesound pressure level over the coverage area from the loudspeakerlocation, and dividing the computed amount of acoustic power by a powercapacity of a model of transducer. Computing the curvature of thediffraction slot includes: (a) dividing the coverage area into aplurality of strips corresponding to the number of transducers, (b)locating a first modeled source having a length and an axis with a firstend of its length on a plane joining the loudspeaker location to theback of the coverage area and its axis pointed at a central position ina first of the plurality of strips associated with the rear of thecoverage area, (c) locating a next modeled source having a length and anaxis with a first end of its length coincident with a second end of thefirst modeled source's length and its axis pointed at a central positionin a next of the plurality of strips adjacent to the first of theplurality of strips, and (d) repeating step (c) to position additionalmodeled sources relative to each preceding modeled source until thetotal number of modeled sources equals the determined number ofelectro-acoustic transducers, the curvature of the diffraction slotbeing a curve joining all of the modeled sources.

Advantages include providing a single integrated system that provides aspecified acoustic coverage for a particular venue, including at leastpartially-automated design and fabrication of custom loudspeakercomponents.

Other features and advantages will be apparent from the description andthe claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a process for designing a custom loudspeaker.

FIG. 2 shows a perspective view of a model of a loudspeaker in a venue.

FIGS. 3A, 3B, and 7A show schematic side elevations of a model of aloudspeaker in a venue.

FIG. 4A shows a perspective view of a loudspeaker horn constructed fromflat panels.

FIG. 4B shows a side elevation view of the loudspeaker horn of FIG. 4A.

FIG. 4C shows a front elevation view of the loudspeaker horn of FIG. 4A.

FIGS. 5A, 5B, and 6A show flat panels used in constructing a loudspeakerhorn.

FIGS. 6B and 6C show a conic section used in defining the flat panel ofFIG. 6A.

FIG. 7B shows a schematic plan view of a model of a loudspeaker in avenue.

FIG. 7C shows a side elevation of an intermediate model of a loudspeakerhorn.

FIG. 7D shows a front elevation of the intermediate model of FIG. 7C.

FIG. 7E shows a plan view of the intermediate model of FIG. 7C.

FIG. 7F shows a side elevation of a model of a loudspeaker horn.

FIG. 7G shows a front elevation of the model of FIG. 7F.

FIG. 7H shows a plan view of the model of FIG. 7F.

FIG. 7I shows a perspective view of the model of FIG. 7F.

FIG. 8 shows an example transducer manifold element.

FIG. 9 shows a support assembly for components of a loudspeaker withexample transducer manifold elements.

FIGS. 10 and 11 show assembled loudspeakers.

FIG. 12A shows a rear perspective view of a loudspeaker assembly.

FIG. 12B shows a front perspective view of the loudspeaker assembly ofFIG. 12A.

FIG. 13 shows a plan view of two loudspeakers in a venue.

FIG. 14 shows a side elevation view of a loudspeaker array in a venue.

DESCRIPTION

An automated loudspeaker design system uses a process such as that shownin FIG. 1. In using the system, a user begins with an architecturalmodel of the venue, and enters design goals, such as the speakerlocations, the listening area, the desired bandwidth of the sound, andthe sound level to be achieved. A simplified representation of a venueis shown in FIG. 2. The system uses the input parameters to design acustom loudspeaker that will meet the specified design goals. In someexamples, the system goes on to supplement the custom loudspeaker withadditional components, such as bass loudspeakers, amplifiers, andcontrollers. The system may also determine configuration parameters forthose components, such as equalization curves, connection topologies,time delays, and output limits.

In the automated loudspeaker design process 100 of FIG. 1, the userbegins by inputting (102) an architectural model of the venue,represented as a simple rectangular room 152 in FIG. 2. This may be doneby loading a file output from architectural design or CAD software or byusing a user interface provided by the system to create a model of thevenue. One such system is described in U.S. patent application Ser. No.10/964,421, filed Oct. 13, 2004, and incorporated here by reference.Next, the user specifies (104) where one or more loudspeaker 154 will belocated within the venue. By “loudspeaker,” we refer to the completeassembly of active electro-acoustic transducers and passive componentssuch as waveguides, ports, and horns that work together to deliver soundto the venue. In FIG. 2, one loudspeaker 154 is shown as a generallytrapezoidal box corresponding to the horn, the most visible part of theloudspeaker. Generally, there is a limited choice of where to locate theloudspeakers, due to architecture, aesthetics, or other considerations.In some examples, the automated portions of the system may specify oneor more locations for the loudspeakers. The user also specifies (106,108) the listening area 156 and sound pressure level (SPL) required ofthe sound system over the listening area. In some examples, the userspecifies (110) the topology of a loudspeaker, e.g., whether it will bean exponential horn, a line array with an arc, progressive (spiral), orJ-shaped curve, or some other topology. The system described isparticularly well-suited to loudspeakers having elongated diffractionslot sources with a continuously curved shape, i.e., a circularcurvature or a progressive curve, coupled to a large horn or waveguide.Selection of the loudspeaker topology may also be automated, with thesystem selecting the best topology to provide the required coverage.Other user inputs (not shown) may include the bandwidth or type of soundto be produced (e.g., music or voice), identification of multiple zonesof coverage, or types of audio signal input sources, to name a fewexamples.

Given these inputs, the system begins to design (112) the first (if morethan one) loudspeaker, which consists of a source 160 and a horn 158. Asa first step, the system determines (114) initial approximations for thehorizontal coverage angle H and vertical coverage angle V over which theloudspeaker will need to project sound to cover the listening area 156.H and V are determined geometrically from the dimensions of thelistening area and the location of the loudspeaker. In FIG. 2, due tothe unequal length and width of the diffraction slot source 160, V ismeasured between the top and bottom walls of the horn, based on aprojection of those surfaces to their intersection at a hypotheticalpoint source 155 located behind the actual loudspeaker 154, while H ismeasured from the intersection of projections of the side walls, justbehind the back edge of the horn. The vertical coverage angle V is theangle between planes connecting the vertical point source location tothe front and back rows of the listening area. The horizontal coverageangle H is the angle between planes connecting the diffraction slotsource to the right and left sides of the seating area. As describedbelow, the values ultimately used may vary from the initial anglessuggested by the structure of the venue. For a rectangular seating area,the angle H may vary over the height of the horn, as it will be narrowerat the top than at the bottom to cover the same width at the greaterdistance of the back row. For a seating area that widens with distance(with appropriate dimensions), the angle H may be constant over theheight of the horn, the increased coverage with distance matching theincreased width of the back of the seating area. Generally speaking, theangle H varies along the height of the horn according to a functionbased on the variation in coverage area with distance. With asufficiently large number of drivers, extremely complicated seatingareas may be covered quite efficiently.

The system predicts (116) the total radiated power that will be requiredto provide the specified sound level over the listening area. The powerand the coverage angles may be determined independently, or they may beco-dependent. In cases where the diffraction slot source is driven bymultiple acoustic transducers, which we refer to as drivers, the useroptionally selects (118) a number N of drivers to be used. The number ofdrivers may be traded off against the wall length L of the horn (seeFIG. 4A) to achieve the required radiated power. A horn with longerwalls (for given coverage angles H and V) will have a wider mouth,providing control of directivity down to lower frequencies, thusrequiring less power to cover a given area than would a shorter horn. Agiven driver has a fixed amount of power available, so the number ofdrivers needed is affected by the amount of control the horn providesover power distribution and the impedance matching of the driver to freeair provided by the horn. The total length of the source, determined bythe number of drivers and their dimensions, also affects the efficiencywith which it delivers the power provided by the drivers. In many cases,the dimensions of the horn are constrained by the architecture and byvisual considerations, and the number of drivers is dictated by thepower required to provide the specified SPL over the listening area.Different models of driver may also be specified to deliver differentpower levels. Once H, V, N, and L have been determined or input, thesystem has the information needed to design a source and horn that willprovide the specified coverage.

Geometrically, the transducing mechanism may be distant from theaperture or surface that radiates sound, as described below. We refer tothe radiating apertures or surfaces that are arranged in a line to formthe diffraction slot source as “sources” to differentiate them from the“drivers” that actually transduce electric signals into acousticpressure. It is the arrangement of these “sources” that is discussedhere in reference to FIGS. 1 through 3. Generic speaker symbols are usedto represent the sources in FIG. 3 without implying any particulartransducer technology or geometric relationship between the drivers andthe sources. The precise positioning of the drivers may be independentof the positioning of the sources, and is described later with referenceto FIGS. 8 through 10. For this discussion of the algorithmic design ofthe loudspeaker, the sources may be considered as drivers locateddirectly at the diffraction slot, as illustrated.

For a circular arc-shaped diffraction slot, the N sources are simplypositioned (120) in an arc, with the angular extent of the arccorresponding to the total vertical coverage angle V, and the radiusdictated by the number of sources N that must be fit into the arc atthat angle and their heights.

For a diffraction slot with a progressive curve shape, where the radiusof curvature varies with position, there are several methods that may beused to determine the angles and positions of the constituent sources.In some examples, the angles are determined following an arithmetic orother mathematical progression, such as a geometric series, and theirpositions are set to form a continuous source along that curve.

In another example, the system may use a model illustrated by FIG. 3Aand described below to design the curved diffraction slot and positionthe sources. The illustration of horn positioning in FIGS. 7A and 7B mayalso be informative for this discussion. Given H, V, and the requiredpower over the listening area, the system divides (120 a) the listeningarea 156 into N equal-power strips 162 i (in the case of FIG. 3A, N=7,so there are seven strips 162 a-162 g) along the length of the listeningarea, each spanning its full width, and lays out an array 170 of Nsources (160 a-160 g in FIG. 3A) corresponding to the strips 162 i. Fora given power available from the drivers and a properly dimensionedhorn, each source can illuminate an area, perpendicular to the source'saxis, of a particular size (an equal-sized area at a greater distancecalls for a narrower horn, constraining the power to a narrower solidangle). The strips 162 i represent portions of the listening area thatare provided the same sound levels from sources driven by drivers ofuniform power. Whether the strips increase, decrease (as shown), ormaintain constant depths with increasing distance from the loudspeakerdepends on a number of factors, including whether the listening areaincreases or decreases in width, the angles between the loudspeaker andeach strip, and how well the loudspeaker controls dispersion atincreasing distances. The sources 160 i are aimed (120 b) to each covertheir respective strip 162 i, and arranged to form a continuous curve.

In some examples, the listening area is divided into the equal-powerstrips as follows. FIG. 3B shows a detail of one strip 162 g from FIG.3A, with additional measurements indicated. When the loudspeaker isprojecting to the listening area strip 162 g at an angle, the listeningarea is covered by a projected area 180 g that is perpendicular to thedirection of radiation, indicated by axis 164 g. The projection to thelistening area strip 162 g is bounded by front and rear planes 182 a and182 b. For a small section of the listening area at a downward angle vfrom the loudspeaker, which we call the coverage area Ac, the projectedarea Ap(v) is computed from the coverage area Ac(v) and the incidentangle θ:

A _(p)(v)=A _(c)(v)×cos(θ)  (1)

The power required to provide the specified direct-field intensity Id isequal to the intensity times the area covered. For a loudspeaker that isclose enough to the listening area that the angle of incidence variesappreciably from the front of the listening area to the back, the actualcoverage areas vary with angle (which in turn varies with position),even while projected areas remain constant with distance, so we computean integral over the listening area (i.e., between vertical angles v0 atthe front and vn at the rear) to find the total required power:

W _(req)=∫_(v) ₀ ^(v) ^(n) I _(d)(v)A _(c)(v)cos(θ)dv.  (2)

The function defining A_(c)(v) in the integral (2) depends on thegeometry of the venue and the loudspeaker location, as does θ.Direct-field intensity Id may also be a function of the position in thelistening area, or it may be constant. The particular solution to theintegral will therefore be based on the inputs to the process 100, andit may be solved numerically or algebraically, depending on thecapabilities of the system carrying out the process 100.

The required power W_(req) is divided by the nominal power W_(s)provided by one driver to find a lower bound for N, that is:

$\begin{matrix}{N \geq {\frac{W_{req}}{W_{s}}.}} & (3)\end{matrix}$

The user may specify a larger value of N, or may choose to at leaststart with the computed minimum value. The listening area is thendivided up into the equal power strips 162 i by solving the integral (2)for values of v₁ and v₂ that define an area covered by the power W_(s)of one driver:

W _(s) =∫v ₁ ^(v) ^(n) I _(d)(v)A _(c)(v)cos(θ)dv.  (4)

Starting at the rear of the listening area, where v₂ is known (i.e., forthe first strip, v₁=v_(n)), the integral (4) is solved iteratively foreach strip 162 i, with the previous slice's lower angle v₁ becoming thenext slice's upper angle v2. If the user has specified a larger for Nthan that required by (3), then W_(s) in (4) can be replaced byW_(req)/N_(user). As the angles vary, the areas of the actual coverageareas will vary, while the projected coverage area is the same for eachactual coverage area. In some examples, such as where the loudspeaker islow to the ground and the angles of incidence quite severe, additionalnumeric calculations may be needed for each source and coverage area,rather than the simplifications just noted. In the case of a singlehorn, the actual coverage areas are rectangular (or nearly-rectangular)strips spanning the width of the listening area and having varyingdepths, as shown in FIG. 3. The dimensions used in FIG. 3 are arbitrary,and selected only to illustrate the process. If multiple loudspeakersare to be used, the strips may cover less than the full width of thelistening area. Once the strips have been found, the sources are eachaimed (120 b) to cover their corresponding strip.

An iterative process may also be used to determine the positions of thesources and define the curve of the total diffraction slot source. Afirst source 160 a is positioned with its top edge defining the top endof the curve. This source begins the curve just above the planeconnecting the point source 155 to the back row, so that the drop off inenergy (typically −6 dB) at the edge of the projected coverage areafalls outside the listening area. The source 160 a is tilted such thatits axis 164 a passes through the center of the rear-most strip 162 adefined in (4), thus defining the source's pitch angle. The pitch anglefor each source will correspond to the angle v at the center of thecorresponding strip, used in the calculations above. From the top edgeposition, pitch angle, and the dimensions of the source, the location ofthe first source's lower edge is known. The next source is positionedwith its top edge at the lower edge of the previous source, and theabove steps are repeated. This continues until all sources arepositioned, producing the progressive curve seen in FIG. 3. The finalsource will be located with its bottom edge extending just beyond theplane connecting the point source 155 to the front row. The drop-off inpower at the edges of the coverage areas is compensated for betweensources by the overlap that results in the coverage of adjacent sources.The areas computed above will result in angles between sources thatproperly overlap the projected areas of each source, using theoverlapping coverage of the sources to provide even coverage in thetransition regions. The same process could be applied starting with thelowest source 160 g and the front-most strip 162 g, and the process maybe varied to meet other goals, if, for example, uniform intensity overthe listening area is not desired.

Once the diffraction slot source provided by the arc of sources isdefined, the horn walls are designed to confine the sound radiated bythe sources to the listening area. A generalized horn 158 is shown inFIGS. 4A-4C. Independently of the source curvature, the horn 158 mayhave a complex shape that is narrower and deeper at the top, forprojecting sound to the back of a venue, and wider and shallower at thebottom, for spreading sound over the front of the venue. This allows asingle loudspeaker to cover a significant portion of the listening area.In other examples, the horn maintains the same shape from top to bottom.To define the walls of the horn 158, flat top and bottom panels 166, 168are positioned (122) in planes separated by the vertical coverage angleV to align with the top and bottom of the listening area 156 (FIG. 2)(more generally, the panels 166 and 168 may be referred to as endpanels, as the loudspeakers may be installed in various orientations).Side walls 200 of the horn 158 are next defined (124) to align with thesides of the listening area 156. The side walls 200 are separated by thehorizontal coverage angle H, which as noted above, may vary with height.To accommodate the curved source defined in the previous steps, the sidewalls 200 are also curved. In the horn fabrication process describedbelow, the side walls are formed from flat panels and bent to the neededcurved shape. In some examples, the ideal curve of the side walls putstoo much stress in the material, so the curve of the side walls issoftened (124 a) from the ideal shape as needed. If additionalloudspeakers are called for, they are designed (113) following the sameprocess, iteratively or in parallel with the first loudspeaker.

Once the horn geometry has been determined, it may be refined. Soundsystem simulation software may be used (126) to determine equalizationparameters and predict the radiation pattern of the loudspeaker. Thepredicted radiation pattern is then offered (128) to the user, eithergraphically, as described, for example, in U.S. patent application Ser.No. 10/964,421 or through an audio simulation, as described, forexample, in U.S. Pat. No. 5,812,676, both incorporated here byreference. The user chooses (130) to accept the design to or makechanges to one or more of the parameters (H, V, N, or L, or one or moreof the original input parameters). For example, changing the number ofdrivers, the wall length, or the coverage angles may result in asmoother radiation pattern. If too many drivers are specified for thebudget, the user might decrease the specified sound level;alternatively, if there is room in the budget, the user might directlyspecify more drivers or might raise the specified sound level. Ifchanges are made, the process iterates the source and horn design stepsto produce and simulate a new design. In some examples, the iteration isalso automated. If the predicted radiation pattern does not match theinput parameters within some threshold, the process uses the differenceto refine the values of H, V, N, or L, and then repeats the appropriatesteps to alter the shape of the source and horn according to the refinedvalues. This may repeat until the values converge, that is, thedeviation from the target, improvement per iteration, or the changescalled for to further refine the design are less than some threshold.Once the horn shape is accepted (130), the side walls are mathematically(analytically or numerically) transformed (132) into flat shapes. Plansfor the top, bottom, and side walls are output (134) for fabrication(136), described below.

In some examples, the loudspeaker design process 100 is paired with asystem configuration process 138 that uses the same or similar inputsand outputs configuration parameters such as equalization settings, timedelays, limiter levels, bills of material, schematics, and the like. Anautomated process for system configuration is described in U.S. Pat. No.7,206,415, incorporated here by reference. Configuration 138 may also beperformed manually. Finally, the system is installed (140) and put touse.

A particular loudspeaker well-suited for customization and, inparticular, the automated design process described above, is shown inFIGS. 5 through 10. FIGS. 5A, 5B, and 6A show flat panels that might bedesigned according to the process described above and assembled to formthe horn shown in FIGS. 4A-4C. In particular, the side panel 200 in FIG.6A is joined to top and bottom panels 166 and 168 like those in FIGS. 5Aand 5B to form a horn for use with a circular arc source. The process ofdetermining the shape of these panels is described below. Creation of ahorn for a progressive curve from similar materials is described fartherbelow with reference to FIGS. 7A through 7I. A set of modular manifoldsections, such as those shown in FIG. 8, couple to the transducers'respective radiating apertures or surfaces and are assembled on a rigid,curved keel shown in FIG. 9 to form the curved diffraction slot sourcethat is joined to the horn 158 to form the complete loudspeaker 154,shown in FIG. 10. While loudspeakers of this type may be designed andbuilt manually, they are well-suited to the automated process describedherein, which deterministically designs the speakers based on the inputperformance and venue parameters.

The horn 158 is formed from four surfaces that begin as flat panels andare joined to form the complex curvature needed. As shown in FIGS. 5Aand 5B, the top and bottom panels 166 and 168 are triangles (with theirtips truncated) with side edges 202, 204, 206, and 208. The centralangles of the triangles determine the horizontal coverage angle H of thehorn. If the triangular end panels 166 and 168 are identical (not asshown), then the horizontal angle will be constant along the height ofthe horn. If the end panels are not identical, the curvature of the sidewalls will be more complex and H will vary along the height of the horn.One end may be narrower and deeper, while the other end is wider andshallower, though width and depth may be independent. Such a complexcurvature provides the long and narrow top and short and wide bottomdescribed above. In an even more complex curvature, the paired edges 202and 204 of the top panel 166 may be different lengths from the edges 206and 208 of the bottom panel 168, causing the wall length L to vary alongthe height of the horn. This may provide, for example, a horn with anarrow end and a wide end, but with the same depth at both ends. In theexample shown, the triangles and therefore the horn are symmetric aboutone axis, but this is also not a requirement. The horn may be asymmetricin the horizontal plan, in which case the opposite edges 202/204 and206/208 of each triangle will be different.

FIG. 6A shows the flat side panel 200 that will be joined to thetriangular end panels 166 and 168 to form a horn fitting a source with acircular curvature. The panel 200 is a section of an annulus, defined byan inner circumferential section 210 with a radius R₁ from a centerpoint 211, an angle V_(f) between two edges 212 and 214, each of lengthL (the depth of the horn), and an outer circumference 216 at a radiusR₂. Joining two panels 200 such that the inner edges 210 of the twopanels remain parallel while the panels diverge at the horizontalcoverage angle H imposes a curvature on the panels along their verticalextent. As shown in FIG. 6B, the side panels 200 for such a horn eachcorrespond to a section of the surface of a section of a cone 220 (onlypart of the cone is shown). FIG. 6C is the same as FIG. 6B with only onepanel 200 shown for clarity. The cone has an apex 221, and the surfacedefining side wall panel 200 is a band with its edges 212 and 214 lyingon lines 222 and 224, and with the inner circumferential edge 210 andouter circumferential edge 216 forming parallel circular arcs on thesurface of the cone 220.

The dimensions of the side panel 200 are determined by certain aspectsof the cone 220, which are in turn determined by the starting values H,V, N, and L, defined earlier. In FIG. 6B, a horizontal plane 228 definesthe inner edge 210 by its intersection with the cone. The plane 228contains the arc of the curved diffraction slot source (not shown),which will normally be vertical when installed. The side panel 200extends away from the plane 228 towards the base of the cone. In FIG.6B, the second side panel is offset a small amount from the cone,representing the width of the diffraction slot source—a second conecorresponding to the second panel is not shown.

The angle between the side panel 200 and the plane 228 is H/2, as eachside panel 200 is one-half the horizontal coverage angle H from thecenter plane 228. Because plane 228 is perpendicular to the axis 230 ofthe cone, H/2 is also the base angle of the cone. The vertical coverageangle V of the horn matches the angle in the plane 228 between planesdefining the end panels 166 and 168, which intersect at the axis 230(while the planes aren't shown, they correspond to the near and farfaces of the illustrated section of the cone 220). As noted, the lengthof the edges 212 and 214 is L, directly defining the length of the hornwalls. (The far edge 214 of the lower panel 200 is obscured, but bothedges 212 and 214 are visible and labeled on the upper panel and in FIG.6A.)

The inner circumferential edge 210 connects a number of line segments210 a matching the number of drivers N, each of which has a length B.Projecting a perpendicular segment 234 from the center of one segment210 a back to the axis 230 of the cone forms a right triangle having abase of length B/2 and a hypotenuse 238. The length R_(s) of thehypotenuse 238 is the radius in the plane 228 of the innercircumferential edge 210 when the panel 200 is bent to conform to thecone. The angle of this triangle, at the axis 230, is

$\frac{1}{2}\frac{V}{N}$

(as the angle V is divided into N segments, and this triangle furtherdivides one of those in half), and the base length is B/2, so the lengthof hypotenuse 238 is found as:

$\begin{matrix}{R_{s} = {\frac{B}{2{\sin \left( {\frac{1}{2}\frac{V}{N}} \right)}}.}} & (5)\end{matrix}$

The value of the inner radius R₁ and of the angle V_(f) between theedges 212 and 214 of the flat panel 200 in FIG. 6A are found from thefact that when the conic surface is laid flat, the edge 210 is remainscircular, but with a different radius R₁ than that it had in the cone,R_(s). As a result, the arc length of edge 210 is the same in bothfigures, thus:

R ₁ V _(f) =R _(s) V.  (6)

The segment of the line 222 from the corner of the panel 200 to the apex221 also has length R₁. This segment can be seen to form a righttriangle with the radius 238 b and the axis 230 of the cone. Knowing theangle H/2 between the plane 228 and the surface of the cone, the lengthfrom the apex 221 to the edge 210 is found as:

$\begin{matrix}{R_{1} = {R_{s}{\frac{1}{\cos \left( \frac{H}{2} \right)}.}}} & (7)\end{matrix}$

Solving (4) and (5) for V_(f),

$\begin{matrix}{V_{f} = {V\mspace{14mu} {{\cos \left( \frac{H}{2} \right)}.}}} & (8)\end{matrix}$

Combining (5) and (7), R₁ is also found in terms of the inputs:

$\begin{matrix}{R_{1} = {\frac{B}{2{\sin \left( {\frac{1}{2}\frac{V}{N}} \right)}{\cos \left( \frac{H}{2} \right)}}.}} & (9)\end{matrix}$

Given V_(f), R₁, and L, the panel 200 can be cut from a flat sheet, asit is simply a section of an annulus having inner radius R₁, outerradius R₂=R₁+L, and included angle V_(f).

The horn shown in FIG. 6B maintains a constant angle H, such that thetop and bottom panels 166 and 168 are identical. Once a panel isdesigned according to the cone's geometry, however, it may be used in ahorn having a varying horizontal angle by using top and bottom panelswith differing angles. To design a horn that varies in length L alongits height, the outer radius R₂ may be varied with position,independently of whether H will be varied as well. In such a case, theouter radius R2 may vary monotonically from one end to the other, thatis, it will increase or decrease, depending on point of view. If L and Hare varied together, such that the walls lengthen as the horizontalangle decreases, a horn may be formed with a varying angle but stillhaving a rectangular mouth, or even having a mouth that gets wider asthe angle gets narrower.

A second method of forming the horn sides begins with a series of flatshapes. This method is useful, for example, with a J-curve, progressivecurve, or other complex source. As shown in FIGS. 7A through 7E, thehorn 158 can be conceptually divided into a series of stacked sub-horns158 i, one for each driver. FIGS. 7A and 7B show only the top and bottomsub-horns 158 a and 158 g (for a seven driver horn), for clarity. Itshould be noted that these figures are not to scale within or betweenfigures. Each sub-horn has its own horizontal and vertical coverageangles, Hi and Vi, based on the relationship between its location andthe corresponding strip 162 i of the listening area, explained abovewith regard to FIG. 3. A stack of such sub-horns 158 i is modeled asshown in FIGS. 7C through 7E. Initially, each sub-horn is modeled hashaving a rectangular mouth, formed by smaller, flat versions of the sidewalls and its own triangular top and bottom panels. In a simplifiedcase, the side walls may be initially modeled as trapezoidal or assections of annuli found as described for a circular arc source, above,each with an N of 1 and H, V, and L set according to the coverage areaof strip 162 i. As seen in FIGS. 7A and 7B, the top and bottom panelsare positioned to begin at the upper and lower edges of their respectivesources 160 a, 160 g (determined at steps 120 a and 120 b of process100, above) and align with the top and bottom ends of the correspondingslices of the listening area (as noted with regard to the sourcelocating process, the actual coverage areas are typically extended justbeyond the limits of the listening area, to account for the drop-off inpower at the edges of the coverage areas). Dashed lines corresponding tothese coverage areas are shown for sources 160 a and 160 g in FIG. 7A.The angle between these lines, projected back to their intersection,will be the Vi for that sub-horn (the intersection of thenearly-parallel top and bottom lines for strip 162 a would be far offthe page, so those lines are shown truncated). It should be noted thatbecause all three axes in the figures are drawn to different scales, asare the different components, the geometrical relationships in thefigures may not match a real-world implementation. Joining together sucha stack of sub-horns with different vertical coverage angles allows amore uniform frequency response over the entire listening area.

Once the stack of sub-horns is modeled, their trapezoidal side-walls aredeformed to meet at their edges and corners to form a sheet, and curvedto provide the sheet with a continuous curvature, as shown in FIGS. 7Fthrough 7I. Dashed lines show the edges of the deformed and mergedsegments. Various techniques may be used to join the panels, such asaveraging lengths, matching mid-points, or moving each bottom corner outto the adjacent top corner, to name some examples. The top and bottompanels of each modeled sub-horn (except the outermost top and bottompanels) are removed, leaving a single open mouth. In some examples, oneor more of the intermediate top and bottom panels or smaller bracingmembers may be retained to lend structural stability to the horn andmaintain the designed horizontal angle H. If the curvature of the sidepanel generated by this process exceeds what is possible or structurallysound for the material to be used, then the curvature may be modified,such as by widening or narrowing the horn to remove inflection points(where curvature changes from convex to concave) or decreasing radiuses.In some examples, it has been found that extremely complex curvaturesare possible, as long as there remains at least one direction at anygiven point where the local relative curvature is zero.

To form a complex curvature from flat panels, the side panels 200 arefabricated from a thin, flexible material having enough stiffness tomaintain a relatively rigid finished assembly, once the ends are fixedto the less-flexible top and bottom panels, which are in turn fixed tothe keel. In some examples, PVC sheets having a thickness of 3.18 mm(0.125 in) have been found to have a suitable stiffness. Aluminum sheetshaving a thickness of 1.27 mm (0.050 in) have also been found to have asuitable stiffness, though metals may not have enough internal loss toprevent sound from escaping through the walls. The triangular end panels166 and 168 are not curved in this example, and can therefore be madefrom stiffer or thicker flat material. We have found that plastic sidewalls prevent even very high pressure sound from escaping through thewalls, despite the thin material. We believe this may be due to thestressed curvature of the side walls increasing their rigidity onceassembled, together with a high internal loss in the material. By“flexible,” we refer to material that can be bent to the desired shapewhile remaining within the elastic limits of the material, that is,there is no plastic deformation or cracking when bending the sheets toshape. In contrast, by “rigid” we refer to material having sufficientstiffness that it will impart the stress needed to maintain the bentshape of the parts it supports without being bent or otherwise deformeditself. It is preferred that all the materials used in the horn beenvironmentally stable. In some examples, a horn may need a smallvertical angle and flat top and bottom ends, resulting in side wallswith minimal curvature in the vertical direction. In order to add thestress needed for stiffness in this case, the side panels may be given acurvature in the horizontal direction, i.e., the horn width flaresoutward along a curve.

In some examples, the top and bottom panels may be curved. In such acase, the side panels may also be curved or may remain flat, dependingon the particulars of the horn. For example, for very small verticalangles, the diffraction slot may have little curvature, resulting ingenerally flat side panels, while the top and bottom panels may becurved to flare away from the diffraction slot. In such a shape, theends of the side panels would be curved, rather than straight, toconform to the curved end panels. If the curved end panels are formedfrom a rigid material, then the structure may remain as described above.On the other hand, if the end panels are formed from a flexiblematerial, then the side panels may need to be rigid in order to supportthe curvature of the end panels. Alternatively, the joint between thekeel and the curved edges of the side panels may impart sufficientrigidity that all four panels may be flexible and hold each other toshape, in tension.

The audio source for use with the horn 158 in the complete loudspeakeris a curved diffraction slot driven by a set of electro-acoustictransducers. The transducers may be, for example, compression drivers,cone-type transducers, electro-static transducers, or other types ofelectro-acoustic transducers. The diffraction slot source is formed bystacking a number of modular manifold components that each couple matedtransducers to a slot-shaped outlet. An example manifold component 300is shown in FIG. 8. In this example, each manifold component 300 has twomounting plates 302 where compression drivers (not shown) are attached.The compression drivers direct sound energy into openings 304 into ducts306. The ducts 306 end at a rectangular aperture 308. When a number ofmanifold components 300 are stacked, as shown in FIGS. 9 (with adifferent example manifold component 301) and 10, the apertures 308together form the diffraction slot source. By moving the transducersaway from the diffraction slot, and to the space behind the side wallsof the horn, where there is more room, the manifold components 300 allowlarger transducers to be used than if the transducers were directlylocated at the diffraction slot. While the example of FIG. 8 shows atwo-sided manifold, single-sided manifold components may also be used,alternating sides as shown in FIGS. 9 and 12, to accommodate even largerdiameter transducers.

In some examples, a rigid keel 320, shown in FIG. 9, is used to providestructure for aligning the manifold components in the desired curvatureand joining them to the horn 158. In the example of FIG. 9, single sidedmanifold components 301 are shown, as opposed to the two-sidedcomponents 300 of FIG. 8. Each manifold component 301 couples a singledriver (not shown) to the diffraction slot, with alternating manifoldsections bending to opposite sides of the loudspeaker, accommodatingdrivers with a larger diameter. The keel 320 may also provide astructural “back bone” for the horn. In some examples, the keel isassembled from steel panels 322, 324, 326, 328 which provide a rigidsupport for anchoring the other components and hanging the assembledloudspeaker. In some examples, the keel is formed from two curved partsthat simply sandwich the manifold components. In the example of FIG. 9,the manifold components are not anchored to the sides of the keel—thesides of the keel project forward of the manifold openings and will bepositioned to either side of the rear of the horn, while the manifoldcomponents will meet the edges 210 of the side walls.

The components described above are assembled to form a completeloudspeaker 154, as shown in FIG. 10. The keel 320 is attached to thebase of the horn 158. A stack 330 of manifold components 300 is attachedto the keel 320 with their apertures 308 mating to the opening in thehorn to form the diffraction slot source. Each manifold component ismated to at least one driver 184. In the example of FIG. 10, thetwo-sided manifold components of FIG. 8 are used, so two drivers areused with each manifold component, though only the top one on the farside is visible in the figure.

The area covered by the loudspeaker 154 is determined by the dimensionsof the horn 158. Given a required coverage pattern, the necessarydimensions of the horn 158 can be determined as described above. In someexamples, as shown in FIG. 11, multiple loudspeakers 154 a, 154 b havinghorns 158 a, 158 b with different horizontal and vertical angles andlengths, and manifold stacks 330 a, 330 b with the same or differentnumbers of drivers, may be stacked. This allows smaller individualcomponents to be used, simplifying fabrication, shipping, and storage ofcomponents. In some examples, the progressive-curve process describedabove would result in too great a curvature in the side panels, so twoor more stacked loudspeakers are used, each providing the coverage ofthe corresponding portion of the modeled single horn. When loudspeakersare stacked in this way, the top and bottom panels of adjacent horns aresufficiently thin that the adjacent diffraction slots are close enoughtogether that they combine to act as a single continuously-curveddiffraction slot.

As noted above, once the dimensions of the horn panels 166, 168, and 200are determined, the system outputs (134) plans, i.e., instructions forfabricating (136) the panels and, in some examples, the keel, from flatstock. In some examples, the system directly outputs machine-readableinstructions for use by an automated fabricator, such as a 2-dimensionalCNC milling machine. The panels and keel may be cut on-demand,decreasing the amount of unique inventory that must be maintained for aninstaller to offer a large, and even unlimited, variety of custom horns.Whether custom-cut or pre-manufactured, the panels may be shipped flatand assembled at the point of installation, decreasing the volume ofspace required for storage and shipping. Various standard constructionmethods may be used to join the panels and other components, dependingon the materials used, such as screws, adhesives, or press fittings.

In one example, the ends of the side panels are fixed to the top andbottom panels with screws, and additional plates are used to fix the topand bottom panels to the keel. Prior to fixing the top and bottom panelsto the keel, the side panels are under decreased stress and may relax toa different shape, such that the edges forming the diffraction slotopening do not remain parallel. To assemble the horn, one end panel,i.e., the top or bottom panel, is fixed to the keel, and the other panelis then drawn toward the other end of the keel. As the free end panel ispulled into position, it forces the side panels to deform to the desiredshape. In some examples, the side panel edges come into the desiredcurvature at the keel and fit into prepared grooves in the keelstructure. Once the free end panel is secured to the keel, the bentedges of the side panels remain pressed into the groove in the keel,forming a tight fitting without the use of additional fasteners, thougha sealant may be needed to fully seal the joint. In other examples, suchas where the keel support structure is wider than the slot opening, thebent edges of the side panels to not meet the keel structure, but coupleonly to the manifold openings.

The large horns described herein, in combination with arrayedtransducers, achieve good directivity control over a wide frequencyrange, in some examples going as high as 20 kHz and as low as 400 Hz,300 Hz, or even 250 Hz. For a complete sound reproduction system,modular bass loudspeakers may be added, as shown in FIGS. 12A and 12B.In the example of FIGS. 12A and 12B, modular bass loudspeakers 500 areshaped to fit partially behind the flare of the horns 158 of theloudspeakers 154. The bass loudspeakers 500 are shaped to fit behindhorns having any flare angle or curvature within the range of possiblehorns, so the same bass loudspeakers 500 are used with any horn madeusing the above process. For example, in FIGS. 12A and 12B, the samebass loudspeakers 500 are used with a relatively narrow upper horn 158 aand a relatively wider lower horn 158 b. In the example of FIG. 12A,each manifold section 502 couples a single driver 504 to the diffractionslot, alternating sides, as in FIG. 9.

By providing good reproduction with controlled directivity down to 400Hz or less from a single type of loudspeaker, and using the bassloudspeakers only for lower frequencies, with some overlap possible, thecrossover point of the system is below or in the lower end of the rangeof human voice (around 300 Hz to 4 kHz). This avoids having adiscontinuity in directivity within the middle of the voice range, asmay be the case when a crossover must be higher in the voice range, suchas around 1-2 kHz. The ability to position the bass loudspeakers closeto the horn loudspeakers and in a precisely controlled relative positionfurther enhances the directivity transition at the crossover point andallows good phase and timing alignment over the full angular range.

FIGS. 13 and 14 show two installation examples that combine several ofthe alternatives mentioned above. In FIG. 13, two asymmetricloudspeakers 154-L and 154-R are used, one on each side of the listeningarea 156. The inner side walls (the side walls facing the middle if thelistening area) of the loudspeakers have a large horizontal angle H₁ toreach the front-center of the listening areas, while the outer sidewalls have narrow horizontal angles H₂ to confine the sound to the outeredge of the listening area with sufficient sharpness to reach the rear.The angles H₁ and H₂ are unequal because the diffraction slot is aimedat the rear-center of the listening area 156, rather than centeredbetween the inner and outer walls of each horn, to provide even soundcoverage. As in the other figures, axes are not to scale and the anglesand distances in FIG. 13 are exaggerated to show their differences.

In FIG. 14, a long array of loudspeakers 154 a-154 d is used to providean extremely long diffraction slot for covering a large venue 152 withtwo listening areas 156 a and 156 b. The uppermost loudspeaker 154 areaches the back of the balcony 156 b, while the lower threeloudspeakers 154 b-154 d cover the lower floor 156 a. In such aconfiguration, circular-arc modules of differing radius may be arrayedto achieve the effect of a long spiral array while using the simplershapes of the circular-arc horn and keel.

Other implementations are within the scope of the following claims andother claims to which the applicant may be entitled.

What is claimed is:
 1. A method comprising: obtaining loudspeaker dataidentifying a number of electro-acoustic transducers to be used in aloudspeaker, horizontal and vertical coverage angles for theloudspeaker, and a wall length for a horn of the loudspeaker; computinga curvature of a diffraction slot of the loudspeaker having a lengthbased on the number of transducers; defining top and bottom end panelsof the horn of the loudspeaker corresponding to the vertical coverageangle; defining first and second side walls of the horn having lengths,widths, and curvatures based on the number of transducers, thehorizontal and vertical coverage angles, and the curvature of thediffraction slot; computing dimensions of flat panels corresponding tothe defined first and second side walls; and outputting machine-readableplans for fabrication of the top and bottom end panels and the first andsecond side walls.
 2. The method of claim 1 further comprising:fabricating flat panels based on the output plans; and assembling theflat panels to form the horn.
 3. The method of claim 2 whereinfabricating the flat panels comprises: inputting the plans to a CNCmilling machine; and operating the CNC milling machine to cut panels ofthin flexible material according to the plans.
 4. The method of claim 3in which the thin flexible material comprises PVC.
 5. The method ofclaim 2 wherein assembling the flat panels to form the horn comprises:securing first and second edges of each of the side wall panels to firstand second edges of the top and bottom end panels; and bending the sidewall panels to conform a third edge of each of the side wall panels tothe computed curvature.
 6. The method of claim 5 wherein bending theside wall panels comprises: securing a first one of the top or bottomend panel to a first end of a curved support structure corresponding tothe computed curvature; and drawing the other of the top or bottom endpanel toward a second end of the curved support structure, such that thethird edges of each of the side wall panels each seat in a groove in thecurved support structure.
 7. The method of claim 1 further comprising:assembling a keel comprising a curved support structure corresponding tothe computed curvature, a plurality of manifold components fixed to thesupport structure, each having an output opening positioned within thesupport structure, the output openings of the plurality of manifoldcomponents together comprising a diffraction slot source, and aplurality of electro-acoustic transducers each fixed to one of themanifold components, each transducer coupled to an input opening of thecorresponding manifold component; and coupling the keel to a horn,fabricated according to the plans, such that the diffraction slot sourceis coupled a diffraction slot opening in the horn defined by edges of atleast the first and second side panels.
 8. The method of claim 1 whereindefining the first and second side walls comprises computing a radius R₁of an inner circumference of an annulus, a radius R₂ of an outercircumference of the annulus, and an angle V_(f) of a section of theannulus, the side walls each corresponding to a section of the annulusbounded by the computed angle.
 9. The method of claim 8 wherein theradius R₁ is computed by applying the formula${R_{1} = \frac{B}{2{\sin \left( {\frac{1}{2}\frac{V}{N}} \right)}{\cos \left( \frac{H}{2} \right)}}},$where B is a dimension of one of the transducers, H is an angle betweenplanes connecting the location of the loudspeaker to sides of thecoverage area, V is an angle between planes connecting the location ofthe loudspeaker to the front and back of the coverage area, and N is thenumber of transducers.
 10. The method of claim 9 wherein the radius R₂is computed by applying the formulaR ₂ =R ₁ +L where L is the length of the horn.
 11. The method of claim 8wherein the angle V_(f) is computed by applying the formula$V_{f} = {V\mspace{14mu} {\cos \left( \frac{H}{2} \right)}}$ where His an angle between planes connecting the location of the loudspeaker tosides of the coverage area, and V is an angle between planes connectingthe location of the loudspeaker to the front and back of the coveragearea.
 12. The method of claim 1 wherein defining the first and secondside walls comprises: modeling a set of sub-horns each corresponding toa section of the diffraction slot and shaped to confine acoustic energyradiated by the section of the diffraction slot to a correspondingsection of the coverage area; and deforming and joining side walls ofadjacent pairs of the trapezoidal sub-horns to define contiguous curvedsheets spanning all of the sub-horns.
 13. The method of claim 12 whereineach of the sections of the coverage area corresponds to a projectedarea perpendicular to a direction of radiation from the correspondingsection of the diffraction slot to the section, all of the projectedareas having substantially the same area.
 14. The method of claim 1wherein the curvature of the diffraction slot comprises a circular arc.15. The method of claim 1 wherein the curvature of the diffraction slotcomprises a curve having a progressively decreasing radius.
 16. Themethod of claim 1 wherein defining the side walls includes modifying thecurvatures of the side walls based on data describing materialproperties of the side walls.
 17. The method of claim 1 whereinobtaining the loudspeaker data comprises: receiving input datadescribing a venue, a location for the loudspeaker in the venue, acoverage area within the venue, and a sound pressure level associatedwith the coverage area; from the input data, determining the number ofelectro-acoustic transducers to be used in the loudspeaker, thehorizontal and vertical coverage angles, and the length of the horn. 18.The method of claim 17 wherein determining the number of transducerscomprises receiving the number of transducers as input from a user. 19.The method of claim 17 wherein determining the number of transducerscomprises: computing an amount of acoustic power necessary to providethe sound pressure level over the coverage area from the loudspeakerlocation; and dividing the computed amount of acoustic power by a powercapacity of a model of transducer.
 20. The method of claim 17 whereincomputing the curvature of the diffraction slot comprises: (a) dividingthe coverage area into a plurality of strips corresponding to the numberof transducers; (b) locating a first modeled source having a length andan axis with a first end of its length on a plane joining theloudspeaker location to the back of the coverage area and its axispointed at a central position in a first of the plurality of stripsassociated with the rear of the coverage area; (c) locating a nextmodeled source having a length and an axis with a first end of itslength coincident with a second end of the first modeled source's lengthand its axis pointed at a central position in a next of the plurality ofstrips adjacent to the first of the plurality of strips; and (d)repeating step (c) to position additional modeled sources relative toeach preceding modeled source until the total number of modeled sourcesequals the determined number of electro-acoustic transducers; thecurvature of the diffraction slot being a curve joining all of themodeled sources.